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We study theoretically the current-voltage characteristics (IVCs) of the Josephson field effect transistor - a ballistic SNINS junction with superconducting (S) electrodes confining a planar normal metal region (N), which is controlled by the gate induced potential barrier (I). The calculations were performed using the computation technique developed earlier for long single-channel junctions in the coherent multiple Andreev reflections (MAR) regime. We find significant difference of the subgap current structure in these junctions compared to the subharmonic gap structure in tunnel junctions and atomic-size point contacts. For long junctions, whose length significantly exceeds the coherence length, the IVC exhibits current peaks at multiples (harmonics) of the difference $\delta_m$ between the static Andreev levels, $eV_n = n\delta_m$. Moreover, the averaged IVC follows the power rather than exponential behavior, and has a universal scaling with the junction transparency. This result is qualitatively understood using an analytical approach based on the concept of resonant MAR trajectories. In shorter junctions whose length is comparable to the coherence length, the IVC has an exponential form common for point contacts, however the current structures appear at the subharmonics of the Andreev interlevel distance, $eV_n = \delta_m/n$ rather than the gap subharmonics $2\Delta/n$., Comment: 10 pages, 11 figures, submitted to Phys. Rev. B

Andreev bound states in superconducting quantum point contacts (QPC) can be accessed for manipulation and measurement by embedding the QPC in a superconducting loop. We discuss the characteristics of such a device suitable for qubit operation, methods of manipulations with the Andreev levels, and qubit coupling.

The influence of a noisy environment on coherent transport in Andreev states through a point contact between two superconductors is considered. The amount of dephasing is estimated for a microwave-activated quantum interferometer. Possibilities of experimentally investigating the coupling between a superconducting quantum point contact and its electromagnetic environment are discussed.

The formation of bound states at surfaces of materials with an energy gap in the bulk electron spectrum is a well known physical phenomenon. At superconductor surfaces, quasiparticles with energies inside the superconducting gap $\Delta$ may be trapped in bound states in quantum wells, formed by total reflection against the vacuum and total Andreev reflection against the superconductor. Since an electron reflects as a hole and sends a Cooper pair into the superconductor, the surface states give rise to resonant transport of quasiparticle and Cooper pair currents, and may be observed in tunneling spectra. In superconducting junctions, these surface states may hybridize and form bound Andreev states, trapped between the superconducting electrodes. In d-wave superconductors, the order parameter changes sign under $90^o$ rotation and, as a consequence, Andreev reflection may lead to the formation of zero energy quasiparticle bound states, midgap states (MGS). The formation of MGS is a robust feature of d-wave superconductivity and provides a unified framework for many important effects which will be reviewed: large Josephson current, low-temperature anomaly of the critical Josephson current, $\pi$-junction behavior, $0\to \pi$ junction crossover with temperature, zero-bias conductance peaks, paramagnetic currents, time reversal symmetry breaking, spontaneous interface currents, and resonance features in subgap currents. Taken together these effects, when observed in experiments, provide proof for d-wave superconductivity in the cuprates., Comment: 52 pages, 20 figures. Review article under consideration for publication in Superconductor Science and Technology

We report the results of an investigation of the effect of the superconducting bound states on coherent multiple Andreev reflections in quantum SNS junctions. A rich resonant structure of the current, associated with the bound states and consisting of peaks, onsets and oscillations, is found by numerical calculations. Positions of the current structures are not given by subharmonics of the energy gap but rather determined by the junction geometry. We present analytical classification of the resonant current structures and calculate their positions and amplitudes. We show that the resonant current structures in three-terminal SNS interferometers can be controlled by external magnetic flux.

We present an extensive experimental and theoretical study of the proximity effect in InAs nanowires connected to superconducting electrodes. We fabricate and investigate devices with suspended gate-controlled nanowires and nonsuspended nanowires, with a broad range of lengths and normal-state resistances. We analyze the main features of the current-voltage characteristics: the Josephson current, excess current, and subgap current as functions of length, temperature, magnetic field, and gate voltage, and compare them with theory. The Josephson critical current for a short-length device, L = 30 nm, exhibits a record high magnitude of 800 nA at low temperature that comes close to the theoretically expected value. The critical current in all other devices is typically reduced compared to the theoretical values. The excess current is consistent with the normal resistance data and agrees well with the theory. The subgap current shows a large number of structures; some of them are identified as subharmonic gap structures generated by multiple Andreev reflection. The other structures, detected in both suspended and nonsuspended devices, have the form of voltage steps at voltages that are independent of either the superconducting gap or length of the wire. By varying the gate voltage in suspended devices, we are able to observe a crossover from typical tunneling transport at large negative gate voltage, with suppressed subgap current and negative excess current, to pronounced proximity junction behavior at large positive gate voltage, with enhanced Josephson current and subgap conductance as well as a large positive excess current., 12 pages, 15 figures

The incoherent regime of Multiple Andreev Reflections (MAR) is studied in long diffusive SNS junctions at applied voltages larger than the Thouless energy. Incoherent MAR is treated as a transport problem in energy space by means of a circuit theory for an equivalent electrical network. The current through NS interfaces is explained in terms of diffusion flows of electrons and holes through tunnel and Andreev resistors. These resistors in diffusive junctions play roles analogous to the normal and Andreev reflection coefficients in OTBK theory for ballistic junctions. The theory is applied to the subharmonic gap structure (SGS); simple analytical results are obtained for the distribution function and current spectral density for the limiting cases of resistive and transparent NS interfaces. In the general case, the exact solution is found in terms of chain-fractions, and the current is calculated numerically. SGS shows qualitatively different behavior for even and odd subharmonic numbers, and the maximum slopes of the differential resistance correspond to the gap subharmonics. The influence of inelastic scattering on the subgap anomalies of the differential resistance is analyzed., 14 pages, 9 figures, title and text revised, to appear in PRB

Single atom junctions between superconducting niobium leads are produced using the Mechanically Controllable Break Junction technique. The current-voltage characteristics of these junctions are analysed using an exact formulation for a superconducting quantum point contact. For tunnelling between two single atoms with a sufficiently large vacuum barrier, it is found that a single channel dominates the current, and that the current-voltage characteristic is described by the theory, without adjustable parameters. For a contact of a single Nb atom it is shown that five conductance channels contribute to the conductance, in agreement with the number expected based on the number of valence orbitals for this d-metal. For each of the channels the transmission probability is obtained from the fits and the limits of accuracy for these numbers are discussed., 11 pages; submitted to Phys. Rev. B

We study the dc conductance and current fluctuations in mesoscopic diffusive SNS junctions at subgap applied voltages $\mathrm{eV}l2\ensuremath{\Delta}$. We find that in spite of the multiple Andreev reflections, the current-voltage characteristic of a long SNINS structure obeys Ohm's law. At the same time, non-equilibrium heating of subgap electrons produces giant shot noise with pronounced subharmonic gap structure which corresponds to stepwise growth of the effective transferred charge. At $\mathrm{eV}\ensuremath{\rightarrow}0$, the shot noise approaches the magnitude of the Johnson-Nyquist noise with the effective temperature ${T}^{\ensuremath{\star}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\Delta}/3$. We analyze the role of inelastic scattering and present a criterion of strong nonequilibrium.

We solve the coherent multiple Andreev reflection (MAR) problem and calculate current-voltage characteristics (IVCs) for Josephson SINIS junctions, where S are local-equilibrium superconducting reservoirs, I denotes tunnel barriers, and N is a short diffusive normal wire, the length of which is much smaller than the coherence length, and the resistance is much smaller than the resistance of the tunnel barriers. The charge transport regime in such junctions qualitatively depends on a characteristic value \gamma = \Delta \tau_d of relative phase shifts between the electrons and retro-reflected holes accumulated during the dwell time \tau_d. In the limit of small electron-hole dephasing \gamma << 1, our solution recovers a known formula for a short mesoscopic connector extended to the MAR regime. At large dephasing, the subharmonic gap structure in the IVC scales with 1/ \gamma, which thus plays the role of an effective tunneling parameter. In this limit, the even gap subharmonics are resonantly enhanced, and the IVC exhibits portions with negative differential resistance., Comment: 8 pages, 3 figures, typos corrected, to be published in Phys. Rev. B

We study the out-of-equilibrium current through a quantum dot which is placed between two superconducting leads held at fixed voltage bias, considering both cases of the absence and the presence of an additional normal lead connected to the dot. Using the nonequilibrium Keldysh technique, we focus on the subgap bias region, where multiple Andreev reflections are responsible for charge transfer through the dot. Attention is put on the dc current and on the first harmonics of the supercurrent. Varying the position and/or the width of the dot level, we first investigate the crossover between a quantum-dot and quantum point-contact regimes in the absence of a normal lead. We then study the effect of the normal electrode connected to the dot, which is understood to lead to dephasing, or alternatively to induce reverse proximity effect. By increasing the dot coupling to the normal probe, we show the full crossover from zero dephasing to the incoherent case. We also compute the Josephson current in the presence of the normal lead and find it in excellent agreement with the values of the nonequlibrium current extrapolated at zero voltage.

Non-dissipative Josephson current through nanoscale superconducting constrictions is carried by spectroscopically sharp energy states, so-called Andreev bound states. Although theoretically predicted almost 40 years ago, no direct spectroscopic evidence of these Andreev bound states exists to date. We propose a novel type of spectroscopy based on embedding a superconducting constriction, formed by a single-level molecule junction, in a microwave QED cavity environment. In the electron-dressed cavity spectrum we find a polariton excitation at twice the Andreev bound state energy, and a superconducting-phase dependent ac Stark shift of the cavity frequency. Dispersive measurement of this frequency shift can be used for Andreev bound state spectroscopy., Published version; 4+ pages, 3 figures

We investigate manipulation with Andreev bound states in Josephson quantum point contacts with magnetic scattering. The Rabi oscillations in the two-level Andreev subsystems are excited by resonant driving the direction of magnetic moment of the scatterer and by modulating the superconducting phase difference across the contact. The Andreev level dynamics is manifested by the temporal oscillation of the Josephson current, which is accompanied, in the case of magnetic manipulation, also by the oscillation of the Andreev states spin polarization. The interlevel transitions obey a selection rule that forbids manipulations in a certain region of external parameters and results from specific properties of Andreev bound states in magnetic contacts: 4pi periodicity with respect to the superconducting phase and strong spontaneous spin polarization.

We study nonequilibrium effects in current transport through voltage biased tunnel junction with long diffusive superconducting leads at low applied voltage, $eV \ll 2\Delta$, and finite temperatures. Due to a small value of the Josephson frequency, the quasiparticle spectrum adiabatically follows the time evolution of the superconducting phase difference, which results in the formation of oscillating bound states in the vicinity of the tunnel junction (Andreev band). The quasiparticles trapped by the Andreev band generate higher even harmonics of the Josephson ac current, and also, in the presence of inelastic scattering, a non-equilibrium dc current, which may considerably exceed the dc quasiparticle current given by the tunnel model. The distribution of travelling quasiparticles also deviates from the equilibrium due to the spectrum oscillations, which results in an additional contribution to the dc current, proportional to $\sqrt{V}$., Comment: 11 pages, 7 figures, to be published in Phys. Rev. B

We present an experimental and theoretical investigation of coherent current transport in wide ballistic superconductor-two dimensional electron gas-superconductor junctions. It is found experimentally that upon increasing the junction length, the subharmonic gap structure in the current-voltage characteristics is shifted to lower voltages, and the excess current at voltages much larger than the superconducting gap decreases. Applying a theory of coherent multiple Andreev reflection, we show that these observations can be explained in terms of transport through Andreev resonances., 4 pages, 4 figures

We present detailed theory for Andreev level qubit, the system consisting of a highly transmissive quantum point contact embedded in a superconducting loop. The two-level Hamiltonian for Andreev levels interacting with quantum phase fluctuations is derived by using the path integral method. We also derive kinetic equation describing qubit decoherence due to interaction of the Andreev levels with acoustic phonons. The collision terms are non-linear due to fermionic nature of the Andreev states, leading to slow non-exponential relaxation and dephasing of the qubit at temperature smaller than the qubit level spacing., 22 pages, 7 figures

We calculate analytically the current statistics for a short diffusive wire between the normal reservoir and a short superconductor-normal metal-superconductor (SNS) junction, at arbitrary applied voltages and temperatures. The cumulant-generating function oscillates with the phase difference $\phi$ across the junction, approaching the normal-state value at $\phi=\pi$. At T=0 and at the applied voltage much smaller than the proximity gap $\Delta_\phi$, the current noise $P_I$ doubles and the third current cumulant $C_3$ is 4 times larger with respect to their values in the normal state; at $eV \gg \Delta_\phi$ they acquire large excess components. At the gap edge, $eV = \Delta_\phi$, the effective transferred charge defined through $dP_I/dI$ and $dP_I/dV$ approaches $0e$ and $3e$, respectively, which makes doubtful the interpretation of these quantities as physical elementary transferred charge. At $T \neq 0$, $C_3$ shows a non-monotonous voltage dependence with a dip near $eV = \Delta_\phi$., Comment: 13 pages, to be published in Proc. NATO ARW "Quantum Transport in Metallic and Hybrid Nanostructures", StPetersburg, 2003

We present theory for a current shot noise in mesoscopic diffusive superconductor-normal metal-superconductor (SNS) junctions. The current shot noise is tremendously enhanced at small applied voltage, V < Δ/e, due to the mechanism of multiple Andreev reflection (MAR), which creates long correlated trains of transmitted electrons. The central result for the MAR regime is a universal value for the noise power in the limit of small voltage and at zero physical temperature, which corresponds to the effective noise temperature of the order of superconducting energy gap Δ. At very small voltage, MAR is destroyed by inelastic relaxation, consequently, the level of noise reduces and approaches at V = 0 the thermal noise value. We investigate the suppression of MAR by inelastic scattering processes and analyze the crossover from the MAR regime to a hot electron regime.

During last decade considerable progress has been made in the investigation and understanding the mechanisms of current transport in mesoscopic superconducting junctions. The term mesoscopic here refers to the junctions where bulk superconducting electrodes in equilibrium (reservoirs) are connected by small nonsuperconducting region with the size smaller than any inelastic mean free path. Such junctions include metallic atomic-size contacts, tunnel junctions, diffusive (metallic) and ballistic (2D electron gas) SNS junctions. A common feature of all these structures concerns the fact that the quasiparticles injected in the junction at zero temperature cannot escape into the reservoir unless the applied voltage is larger than the superconducting energy gap in the reservoir, eV > 2Δ. In 1963, Schrieffer and Wilkins suggested that the necessary energy for the quasiparticle transmission at subgap voltage, eV < 2Δ can be provided by transferring Cooper pairs between the reservoirs [1].

We investigate the dynamics of a two-level Andreev bound state system in a transmissive quantum point contact embedded in an rf-SQUID. Coherent coupling of the Andreev levels to the circulating supercurrent allows manipulation and read out of the level states. The two-level Hamiltonian for the Andreev levels is derived, and the effect of interaction with the quantum fluctuations of the induced flux is studied. We also consider an inductive coupling of qubits, and discuss the relevant SQUID parameters for qubit operation and read out., 4 pages, 1 figure

A theory of coherent multiple Andreev reflections (MAR) is developed for superconductor-normal metal-superconductor (SNS) interferometers. We consider a Y-shape normal electron beam splitter connecting two superconducting reservoirs, where the two connection points to the same superconductor can have different phase. The current is calculated in the quantum transport regime as a function of applied voltage and phase difference, $I(V,\phi)$. MAR in interferometers incorporates two features: interference in the arms of the splitter, and interplay with Andreev resonances. The latter feature yields enhancement of the subgap current and current peaks with phase-dependent positions and magnitudes. The interference effect leads to suppression of the subgap current and complete disappearance of the current peaks at $\phi=\pi$. The excess current at large voltage decreases and changes sign with increasing phase difference.

Spectral density of current fluctuations at zero frequency is calculated for a long diffusive SNS junction with low-resistive interfaces. At low temperature, $T\ensuremath{\ll}\ensuremath{\Delta},$ the subgap shot noise approaches linear voltage dependence, $S=(2/3R)(eV+2\ensuremath{\Delta}),$ which is the sum of the shot noise of the normal conductor and voltage independent excess noise. This result can also be interpreted as the 1/3-suppressed Poisson noise for the effective charge $q=e(1+2\ensuremath{\Delta}/eV)$ transferred by incoherent multiple Andreev reflections (MAR). At higher temperatures, anomalies of the current noise develop at the gap subharmonics, $eV=2\ensuremath{\Delta}/n.$ The crossover to the hot electron regime from the MAR regime is analyzed in the limit of small applied voltages.

Midgap states (MGS) exist at the Fermi level at surfaces and interfaces of d-wave superconductors for order parameter orientations such that a sign change of Andreev reflection can add a (pi) -shift in the Bohr-Sommerfeld quantization condition. MGS are basically robust features, but the detailed density of states, manifested e.g. in zero bias conductance peaks (ZBCP), is in principle a sensitive probe of junctions and interfaces, providing information about normal regions with suppressed order parameter, non-specular scattering from rough or disordered interfaces, impurity states, lifetimes, etc. Resonance coupling of MGS in d45/d+/- 45 SNINS junctions gives rise to large equilibrium Josephson critical current varies direct as (root)D, where D is the normal transparency of the junction. Spontaneous time-reversal symmetry breaking (TRSB) in d0/d45 junctions at low temperatures kBT > (epsilon) 0/(lambda) .

We study theoretically the ac Josephson effect in voltage biased planar junctions of d-wave superconductors. For some orientations of the superconductors a current peak is found at finite voltage in the current-voltage characteristics. We pick out the relevant physical processes and write down an analytical formula for the current which clearly shows how the midgap state acts as a resonance and produces the peak. We present a possible explanation for the zero-bias conductance peak, recently found in experiments on grain boundary junctions of high-temperature superconductors, in terms of resonant transmission through midgap state of quasiparticles undergoing multiple Andreev reflections. We note that within our framework the zero-bias conductance peak appears in rather transparent Josephson junctions of d-wave superconductors., 10 pages, 5 figures, Submitted to a special volume of "Superlattices and Microstructures"

We show that irradiation of a voltage-biased superconducting quantum point contact at frequencies of the order of the gap energy can remove the suppression of subgap dc transport through Andreev levels. Quantum interference among resonant scattering events involving photon absorption is furthermore shown to make microwave spectroscopy of the Andreev levels feasible. We also discuss how the same interference effect can be applied for detecting weak electromagnetic signals up to the gap frequency, and how it is affected by dephasing and relaxation., Submitted to a special volume of "Superlattices and Microstructures" on Mesoscopic Superconductivity

We investigate the properties of subharmonic gap structure (SGS) in superconducting quantum contacts with normal-electron resonances. We find two distinct new features of the SGS in resonant junctions which distinguish them from non-resonant point contacts: (i) The odd-order structures on the current-voltage characteristics of resonant junctions are strongly enhanced and have pronounced peaks, while the even-order structures are suppressed, in the case of a normal electron resonance being close to the Fermi level. (ii) Tremendous current peaks develop at $eV=\pm 2E_0$ where $E_0$ indicates a distance of the resonance to the Fermi level. These properties are determined by the effect of narrowing of the resonance during multiple Andreev reflections and by overlap of electron and hole resonances., Comment: 13 pages, 10 figures

We discuss how to control dc Josephson current by influencing the structure and nonequilibrium population of Andreev levels via external electrostatic gates, external current injection and electromagnetic radiation. In particular we will consider the "giant" Josephson current in "long" SIS tunnel junctions and the regular and anomalous nonequilibrium Josephson currents in three terminal SNS junctions. We will briefly discuss applications to the Josephson field effect transistor (JOFET) and to the newly invented Josephson interference transistor (JOINT)., Comment: 10 pages, 3 figures; contribution to a special volume of Superlattices and Microstructures journal (ed. P.F. Bagwell)

We analyze the variation of the critical Josephson current with gate voltage in a ballistic SNS heterostructure. With increasing gate voltage the number of bound Andrev levels increases, the junction becomes effectively long, and the critical current is suppressed.